Feature Tracking by Two-Step Optimization

Tracking the temporal evolution of features in time-varying data is a key method in visualization. For typical feature definitions, such as vortices, objects are sparsely distributed over the data domain. In this paper, we present a novel approach for tracking both sparse and space-filling features. While the former comprise only a small fraction of the domain, the latter form a set of objects whose union covers the domain entirely while the individual objects are mutually disjunct. Our approach determines the assignment of features between two successive time-steps by solving two graph optimization problems. It first resolves one-to-one assignments of features by computing a maximum-weight, maximum-cardinality matching on a weighted bi-partite graph. Second, our algorithm detects events by creating a graph of potentially conflicting event explanations and finding a weighted, independent set in it. We demonstrate our method's effectiveness on synthetic and simulation data sets, the former of which enables quantitative evaluation because of the availability of ground-truth information. Here, our method performs on par or better than a well-established reference algorithm. In addition, manual visual inspection by our collaborators confirm the results' plausibility for simulation data.